Sunday, February 19, 2017

#clotheslinemath Linear Equations

I am going to teach this lesson on Tuesday to all 3 of my Common Core 8 classes. Any feedback or suggestions prior to that are appreciated. A reflection of how it unfolded to follow. I wanted all the images in one place for my colleagues to use and for anyone else to try. All credit goes to Andrew Stadel and Chris Shores for the lesson, I just added a small extension.

UPDATE: (2/21/17)

I noticed students drew the number line cards really big after looking at the google slides. For each period after I made sure students knew they needed room on their paper for 2 clothesline and 2 graphs to be pasted on.

I had students think for 3 minutes how the 6 parameter cards could be placed on the lower clothesline. I demonstrated how if a card lined up with a number, they would be equal or equivalent. I also demonstrated how you could clip a card underneath another using the clothespin.

I then asked students to place the cards individually with 3 minutes of silent independent work time. Then I timed them for another 3 minutes of taking turns sharing out their ideas to their group, to gain confidence in sharing their idea with the class.

With 6 parameter cards, I said that we would need 6 different students put up 6 different cards and give a statement to the class about what they did and why they chose to put it there. I had students vote using their thumbs whether they agreed or disagreed with a person's statement. I asked students put their thumb sideways if they didn't whether the person was right or wrong. In first period students immediately went for the growth of line 2, or m2, was 0.

Students seemed to see that the blue line's growth had to be 2, because it was the steepest, and it was increasing from left to right so it had to be a positive number, so they said it couldn't be 1 and picked 2. Some students also reasoned that the red line must have a smaller slope but negative because it was decreasing slowly.

One student talked about how the y-intercept of the red line had to be 2, because the blue line was also the same distance from zero being at -2. I asked the students what we call distance from zero, and some remembered that was the absolute value.

After students had placed cards m1 to m3 and b1 to b3, I handed out the desmos graph. I asked them to paste it in their notebook and then see if they agreed with how the clothesline was from the last image. Students noticed that they appeared the same, and the y-intercepts were definitely the same.

I pointed out when students were drawing slope triangles between lattice points, but am not sure if all students correctly did so as I walked around the room.

Students had a bit of trouble with the scale of the graph, with each square being 0.5. This lead them to see that the vertical growth was 1.5, and the horizontal growth was 1. I asked them what the slope triangle was in grid squares, which gave 3/2. Students reasoned that must be between 1 and 2.

I did not get to the part of putting m4 under -1, and b4 under 1. If I had more time I would have. My colleague said his class also had trouble substituting the new m values into the equation y=mx+b to try to confirm that the lines would intersect algebraically.

It was nice to see that after some students noticed the lines would intersect, that they could prove it graphically. In each class a student hung x and y under the respective coordinates for the intersection point.

Some students thought there might need to be 3 sets of x and y coordinates since there were 3 different lines.

Overall I loved the activity. It had a sense of mystery. Also, having a graph with grid lines achieved my goal of practicing calculating slope. I am still concerned how many students left the class with a solid handle on it. I liked how I made sure they had some independent think time before sharing with their group because if it's straight to group it tends to be the same people sharing. Students also liked the chance of going up to the board with the whole class watching, while others were nudged towards giving their reasons for agreeing with someone from their seat.